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Chapter 5 – MBA504 1
Bond and Stock Valuations
Value BondsBond ConceptsPresent Value of Common StocksEstimates of Parameters in the Dividend-Discount
ModelGrowth OpportunitiesThe Dividend Growth Model and the NPVGO ModelPrice Earnings Ratio
Chapter 5 – MBA504 2
Valuation of Bonds and StockFirst Principle:
– Value of financial securities = PV of expected future cash flows
To value bonds and stocks we need to:• Size (how much) and
• Timing (when)
• Discount future cash flows at an appropriate rate:– The rate should be appropriate to the risk presented by the
security.
Chapter 5 – MBA504 3
Definition of a Bond
A bond is a legally binding agreement between a borrower and a lender
Chapter 5 – MBA504 4
• Consider a U.S. government bond listed as 6 3/8 of December 2009.– The Par Value of the bond is $1,000.
– Coupon payments are made semi-annually (June 30 and December 31 for this particular bond).
– Since the coupon rate is 6 3/8 the payment is $31.875.
– On January 1, 2005 the size and timing of cash flows are:
05/1/1
875.31$
05/30/6
875.31$
05/31/12
875.31$
09/30/6
875.031,1$
09/31/12
Chapter 5 – MBA504 5
How to Value Bonds
Discount at the correct discount rate.– If you know the price of a bond and the size
and timing of cash flows, the yield to maturity is the discount rate.
Chapter 5 – MBA504 6
Pure Discount BondsInformation needed for valuing pure discount bonds:
– Time to maturity (T) = Maturity date - today’s date– Face value (F)– Discount rate (r)
Tr
FPV
)1(
Present value of a pure discount bond at time 0:
0
0$
1
0$
2
0$
1T
F$
T
Chapter 5 – MBA504 7
ExampleFind the value of a 30-year zero-coupon bond
with a $1,000 par value and a YTM of 6%.
0
0$
1
0$
2
0$
29
000,1$
30
0
0$
1
0$
2
0$
29
000,1$
30
Chapter 5 – MBA504 8
Level-Coupon BondsInformation needed to value level-coupon bonds:
– Coupon payment dates and time to maturity (T) – Coupon payment (C) per period and Face value (F) – Discount rate
Value of a Level-coupon bond= PV of coupon payment annuity + PV of face value
0
C$
1
C$
2
C$
1T
FC $$
T
Chapter 5 – MBA504 9
ExampleFind the present value (as of January 1, 2004), of a 6-3/8
coupon T-bond with semi-annual payments, and a maturity date of December 2009 if the YTM is 5-percent.
– On January 1, 2004 the size and timing of cash flows are:
04/1/1
875.31$
04/30/6
875.31$
04/31/12
875.31$
09/30/6
875.031,1$
09/31/12
Chapter 5 – MBA504 10
Bond Concepts1. Bond prices and market interest rates move in opposite
directions.
2. When coupon rate = YTM, price = par value.When coupon rate > YTM, price > par value (premium bond)When coupon rate < YTM, price < par value (discount bond)
3. A bond with longer maturity has higher relative (%) price change than one with shorter maturity when interest rate (YTM) changes. All other features are identical.
4. A lower coupon bond has a higher relative price change than a higher coupon bond when YTM changes. All other features are identical.
Chapter 5 – MBA504 11
YTM and Bond Value
800
1000
1100
1200
1300
$1400
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Discount Rate
Bon
d V
alu
e
6 3/8
When the YTM < coupon, the bond trades at a premium.
When the YTM = coupon, the bond trades at par.
When the YTM > coupon, the bond trades at a discount.
Chapter 5 – MBA504 12
Maturity and Bond Price Volatility
C Discount Rate
Bon
d V
alu
e
Par
Short Maturity Bond
Long Maturity Bond
Chapter 5 – MBA504 13
Present Value of Common Stocks
• Dividends versus Capital Gains
• Valuation of Different Types of Stocks– Zero Growth– Constant Growth– Differential Growth
Chapter 5 – MBA504 14
1. Zero Growth
• Assume that dividends will remain at the same level forever
rP
rrrP
Div
)1(
Div
)1(
Div
)1(
Div
0
33
22
11
0
321 DivDivDiv
Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity:
Chapter 5 – MBA504 15
2. Constant Growth
)1(DivDiv 01 g
Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity:
grP
1
0
Div
Assume that dividends will grow at a constant rate, g, forever. i.e.
2012 )1(Div)1(DivDiv gg
3023 )1(Div)1(DivDiv gg
...
Chapter 5 – MBA504 16
3. Differential Growth
• Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter.
• To value a Differential Growth Stock, we need to:– Estimate future dividends in the foreseeable future.– Estimate the future stock price when the stock becomes
a Constant Growth Stock (case 2).– Compute the total present value of the estimated future
dividends and future stock price at the appropriate discount rate.
Chapter 5 – MBA504 17
)(1DivDiv 101 g
Assume that dividends will grow at rate g1 for N years and grow at rate g2 thereafter
210112 )(1Div)(1DivDiv gg
NNN gg )(1Div)(1DivDiv 1011
)(1)(1Div)(1DivDiv 21021 ggg NNN
...
...
Chapter 5 – MBA504 18
)(1Div 10 g
Dividends will grow at rate g1 for N years and grow at rate g2 thereafter
210 )(1Div g
Ng )(1Div 10 )(1)(1Div
)(1Div
210
2
gg
gN
N
…0 1 2
…N N+1
…
Chapter 5 – MBA504 19
A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity. What is the stock worth? The discount rate is 12%.
Chapter 5 – MBA504 20
How to estimate g
g = Retention ratio × Return on retained earnings-- Retention rate: the ratio of retained earnings to earnings
-- Use ROE for return on retained earnings
Chapter 5 – MBA504 21
Growth Opportunities• Growth opportunities are opportunities to invest in
positive NPV projects.• The value of a firm can be conceptualized as the
sum of the value of a firm that pays out 100-percent of its earnings as dividends and the net present value of the growth opportunities.
NPVGOr
EPSP
Chapter 5 – MBA504 22
We have two ways to value a stock:– The dividend discount model.– The price of a share of stock can be calculated
as the sum of its price as a cash cow plus the per-share value of its growth opportunities.
Chapter 5 – MBA504 23
Consider a firm that has EPS of $5 at the end of the first year, a dividend-payout ratio of 30%, a discount rate of 16-percent, and a return on retained earnings of 20-percent.– The dividend at year one will be $5 × .30 = $1.50 per share.
– The retention ratio is .70 ( = 1 -.30) implying a growth rate in dividends of 14% = .70 × 20%
From the dividend growth model, the price of a share is:
Chapter 5 – MBA504 24
First, we must calculate the value of the firm as a cash cow.
Second, we must calculate the value of the growth opportunities.
Finally,
Chapter 5 – MBA504 25
Price Earnings Ratio• Many analysts frequently relate earnings per share to
price.• The price earnings ratio is a.k.a. the multiple
– Calculated as current stock price divided by annual EPS
– The Wall Street Journal uses last 4 quarter’s earnings
EPS
shareper Priceratio P/E
• Firms whose shares are “in fashion” sell at high multiples. Growth stocks for example.• Firms whose shares are out of favor sell at low multiples. Value stocks for example.
Chapter 5 – MBA504 26
Other Price Ratio Analysis– Price/Cash Flow Ratio
• cash flow = net income + depreciation = cash flow from operations or operating cash flow
– Price/Sales• current stock price divided by annual sales per share
– Price/Book (a.k.a. Market to Book Ratio)• price divided by book value of equity, which is
measured as assets – liabilities
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